本文爲筆者在學習周志華老師的機器學習教材後,寫的課後習題的的編程題。之前放在答案的博文中,現在重新進行整理,將需要實現代碼的部分單獨拿出來,慢慢積累。希望能寫一個機器學習算法實現的系列。
本文主要包括:
1、logistics迴歸
2、線性判別分析(LDA)
使用的python庫:
- numpy
- matplotlib
- pandas
Idx | density | ratio_sugar | label |
1 | 0.697 | 0.46 | 1 |
2 | 0.774 | 0.376 | 1 |
3 | 0.634 | 0.264 | 1 |
4 | 0.608 | 0.318 | 1 |
5 | 0.556 | 0.215 | 1 |
6 | 0.403 | 0.237 | 1 |
7 | 0.481 | 0.149 | 1 |
8 | 0.437 | 0.211 | 1 |
9 | 0.666 | 0.091 | 0 |
10 | 0.243 | 0.0267 | 0 |
11 | 0.245 | 0.057 | 0 |
12 | 0.343 | 0.099 | 0 |
13 | 0.639 | 0.161 | 0 |
14 | 0.657 | 0.198 | 0 |
15 | 0.36 | 0.37 | 0 |
16 | 0.593 | 0.042 | 0 |
17 | 0.719 | 0.103 | 0 |
# -*- coding: cp936 -*-
from numpy import *
import pandas as pd
import matplotlib.pyplot as plt
#讀入csv文件數據
df=pd.read_csv('watermelon_3a.csv')
m,n=shape(dataMat)
df['norm']=ones((m,1))
dataMat=array(df[['norm','density','ratio_sugar']].values[:,:])
labelMat=mat(df['label'].values[:]).transpose()
#sigmoid函數
def sigmoid(inX):
return 1.0/(1+exp(-inX))
#梯度上升算法
def gradAscent(dataMat,labelMat):
m,n=shape(df.values)
alpha=0.1
maxCycles=500
weights=array(ones((n,1)))
for k in range(maxCycles):
a=dot(dataMat,weights)
h=sigmoid(a)
error=(labelMat-h)
weights=weights+alpha*dot(dataMat.transpose(),error)
return weights
#隨機梯度上升
def randomgradAscent(dataMat,label,numIter=50):
m,n=shape(dataMat)
weights=ones(n)
for j in range(numIter):
dataIndex=range(m)
for i in range(m):
alpha=40/(1.0+j+i)+0.2
randIndex_Index=int(random.uniform(0,len(dataIndex)))
randIndex=dataIndex[randIndex_Index]
h=sigmoid(sum(dot(dataMat[randIndex],weights)))
error=(label[randIndex]-h)
weights=weights+alpha*error[0,0]*(dataMat[randIndex].transpose())
del(dataIndex[randIndex_Index])
return weights
#畫圖
def plotBestFit(weights):
m=shape(dataMat)[0]
xcord1=[]
ycord1=[]
xcord2=[]
ycord2=[]
for i in range(m):
if labelMat[i]==1:
xcord1.append(dataMat[i,1])
ycord1.append(dataMat[i,2])
else:
xcord2.append(dataMat[i,1])
ycord2.append(dataMat[i,2])
plt.figure(1)
ax=plt.subplot(111)
ax.scatter(xcord1,ycord1,s=30,c='red',marker='s')
ax.scatter(xcord2,ycord2,s=30,c='green')
x=arange(0.2,0.8,0.1)
y=array((-weights[0]-weights[1]*x)/weights[2])
print shape(x)
print shape(y)
plt.sca(ax)
plt.plot(x,y) #ramdomgradAscent
#plt.plot(x,y[0]) #gradAscent
plt.xlabel('density')
plt.ylabel('ratio_sugar')
#plt.title('gradAscent logistic regression')
plt.title('ramdom gradAscent logistic regression')
plt.show()
#weights=gradAscent(dataMat,labelMat)
weights=randomgradAscent(dataMat,labelMat)
plotBestFit(weights)
# -*- coding: cp936 -*-
from numpy import *
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
df=pd.read_csv('watermelon_3a.csv')
def calulate_w():
df1=df[df.label==1]
df2=df[df.label==0]
X1=df1.values[:,1:3]
X0=df2.values[:,1:3]
mean1=array([mean(X1[:,0]),mean(X1[:,1])])
mean0=array([mean(X0[:,0]),mean(X0[:,1])])
m1=shape(X1)[0]
sw=zeros(shape=(2,2))
for i in range(m1):
xsmean=mat(X1[i,:]-mean1)
sw+=xsmean.transpose()*xsmean
m0=shape(X0)[0]
for i in range(m0):
xsmean=mat(X0[i,:]-mean0)
sw+=xsmean.transpose()*xsmean
w=(mean0-mean1)*(mat(sw).I)
return w
def plot(w):
dataMat=array(df[['density','ratio_sugar']].values[:,:])
labelMat=mat(df['label'].values[:]).transpose()
m=shape(dataMat)[0]
xcord1=[]
ycord1=[]
xcord2=[]
ycord2=[]
for i in range(m):
if labelMat[i]==1:
xcord1.append(dataMat[i,0])
ycord1.append(dataMat[i,1])
else:
xcord2.append(dataMat[i,0])
ycord2.append(dataMat[i,1])
plt.figure(1)
ax=plt.subplot(111)
ax.scatter(xcord1,ycord1,s=30,c='red',marker='s')
ax.scatter(xcord2,ycord2,s=30,c='green')
x=arange(-0.2,0.8,0.1)
y=array((-w[0,0]*x)/w[0,1])
print shape(x)
print shape(y)
plt.sca(ax)
#plt.plot(x,y) #ramdomgradAscent
plt.plot(x,y) #gradAscent
plt.xlabel('density')
plt.ylabel('ratio_sugar')
plt.title('LDA')
plt.show()
w=calulate_w()
plot(w)
結果如下:
對應的w值爲:
[ -6.62487509e-04, -9.36728168e-01]
由於數據分佈的關係,所以LDA的效果不太明顯。所以我改了幾個label=0的樣例的數值,重新運行程序得到結果如下:
效果比較明顯,對應的w值爲:
[-0.60311161, -0.67601433]